The concept of dynamical compensation has been recently introduced to
describe the ability of a biological system to keep its output dynamics
unchanged in the face of varying parameters. Here we show that, according to
its original definition, dynamical compensation is equivalent to lack of
structural identifiability. This is relevant if model parameters need to be
estimated, which is often the case in biological modelling. This realization
prompts us to warn that care should we taken when using an unidentifiable model
to extract biological insight: the estimated values of structurally
unidentifiable parameters are meaningless, and model predictions about
unmeasured state variables can be wrong. Taking this into account, we explore
alternative definitions of dynamical compensation that do not necessarily imply
structural unidentifiability. Accordingly, we show different ways in which a
model can be made identifiable while exhibiting dynamical compensation. Our
analyses enable the use of the new concept of dynamical compensation in the
context of parameter identification, and reconcile it with the desirable
property of structural identifiability
